1. bend outwards the ethernet shield reset pin "leg", so that it will not go in the arduino reset socket.
2. solder the 10kOhm resistor between reset pin and the nearby 3.3 Vcc
3. solder the 10nf capacitor between reset pin and ground

Here is a picture of one of my ethernet shields, with the reset "leg" bent outwards.

And this is the details of how I soldered the components on the back of the circuit.
In this position the components are nicely arranged on the back of the board.

With this mod, my arduino + ethernet shield is starting up correctly after powering up, and immediately works with no need of reset button push.

i wanted to test so soldered up the resistor to capacitor for reset lead and stuck the leads into top. but reset issue wasnt resolved. 10nf and 10k used. does it matter brand of ethernet shield? mine has sd card slot yours doesnt in example.

Hi. I managed to have it stable using a 100nF cap, no resistor and the reset pin bent. However it only works when it is powered via the PC USB. If I use a regular 5V USB power supply I still have to reset it.

Hi, thank you for your suggestion. I have tried and I can confirm it's working. But for me, 10 nF capacitor was not enough. Then I was randomly picking some and for me, 1 uF (micro) did the job. No need to hit reset button now after reboot. Thank you!